Subgroups — C₁₃×#18653 #15704992

Order 3328.

918 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1649	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1648	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1476	C₂	1	1	yes	maximal, characteristic
10	Q₈²×C₁₃	—	2	1	no	—
11	C₁₃×#557	C₂²	1	2	yes	—
12	C₁₃×#554	—	2	1	no	—
13	C₁₃×#554	—	2	2	no	—
14	D₄×Q₈×C₁₃	—	2	2	no	—
15	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#544	—	2	2	no	—
17	C₁₃×#544	—	2	1	no	—
18	C₁₃×#533	—	2	1	no	—
19	C₁₃×#533	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₃×#520	—	2	1	no	—
24	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₁₃×#500	—	2	2	no	—
26	C₁₃×#500	C₂²	1	4	yes	—
27	C₁₃×#494	—	2	1	no	—
28	C₁₃×#487	—	2	1	no	—
29	C₁₃×#477	—	2	1	no	—
30	C₁₃×#476	—	2	1	no	—
31	C₁₃×#475	C₂²	1	2	yes	—
32	C₁₃×#474	C₂²	1	2	yes	—
33	C₁₃×#462	C₂²	1	4	yes	—
34	C₁₃×#451	—	2	2	no	—
35	C₁₃×#431	C₂²	1	1	yes	characteristic
36	C₁₃×#428	—	2	1	no	—
37	C₂×C₁₃×#107	—	2	2	no	—
38	C₁₃×#423	C₂²	1	1	yes	characteristic
39	C₁₃×#417	—	2	1	no	—
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#332	C₂²	1	4	yes	—
42	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₃×Q₈⋊C₈	C₂²	1	4	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂×C₁₃×Q₁₆	—	2	4	no	—
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂²×C₈×C₁₃	—	2	1	no	—
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	—	2	4	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	—	2	1	no	—
58	C₁₃×C₄⋊Q₈	—	2	1	no	—
59	C₁₃×C₄⋊Q₈	—	2	1	no	—
60	C₁₃×C₄⋊Q₈	—	2	1	no	—
61	C₁₃×C₄⋊Q₈	—	2	1	no	—
62	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
65	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₁₃×#125	—	2	2	no	—
68	C₁₃×#125	—	2	4	no	—
69	C₁₃×#125	—	2	2	no	—
70	C₁₃×#125	—	2	1	no	—
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	—	2	4	no	—
73	C₁₃×C₂²⋊Q₈	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	—	2	1	no	—
75	C₁₃×C₂²⋊Q₈	—	2	2	no	—
76	C₁₃×C₂²⋊Q₈	—	2	4	no	—
77	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
78	C₄×Q₈×C₁₃	—	2	2	no	—
79	C₄×Q₈×C₁₃	—	2	2	no	—
80	C₄×Q₈×C₁₃	—	2	2	no	—
81	C₄×Q₈×C₁₃	—	2	1	no	—
82	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
84	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×D₄×C₁₃	—	2	4	no	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	—	2	1	no	—
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
90	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#117	—	2	2	no	—
92	C₁₃×#117	—	2	1	no	—
93	C₁₃×#117	—	2	1	no	—
94	C₁₃×#117	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
101	C₂×C₄²×C₁₃	—	2	1	no	—
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×#107	—	2	8	no	—
104	C₁₃×#107	—	2	2	no	—
105	C₁₃×#106	—	2	2	no	—
106	C₁₃×C₄⋊C₈	—	2	1	no	—
107	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
108	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
109	C₁₃×#103	—	2	2	no	—
110	C₁₃×#103	—	2	4	no	—
111	C₁₃×#102	—	2	2	no	—
112	C₁₃×C₂²⋊C₈	—	2	1	no	—
113	C₄×C₈×C₁₃	—	2	1	no	—
114	C₄×C₈×C₁₃	—	2	1	no	—
115	C₄×C₈×C₁₃	C₂³	1	2	yes	—
116	#18653	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₁₃×#41	—	2	2	no	—
118	C₁₃×#41	Q₁₆	1	4	yes	complemented
119	C₂×Q₈×C₁₃	—	2	4	no	—
120	C₂×Q₈×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	2	2	no	—
122	C₂×Q₈×C₁₃	—	2	2	no	—
123	C₂×Q₈×C₁₃	—	2	2	no	—
124	C₂×Q₈×C₁₃	—	4	1	no	—
125	C₂×Q₈×C₁₃	—	8	2	no	—
126	C₂×Q₈×C₁₃	—	8	2	no	—
127	C₂×Q₈×C₁₃	—	8	4	no	—
128	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	4	1	no	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₁₃×Q₁₆	—	8	4	no	—
142	C₁₃×M₁₆	—	4	2	no	—
143	C₂×C₈×C₁₃	—	2	4	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	4	1	no	—
164	C₁₃×C₄⋊C₄	—	4	1	no	—
165	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₁₃×C₂²⋊C₄	—	2	2	no	—
171	C₁₃×C₂²⋊C₄	—	2	1	no	—
172	C₁₃×C₂²⋊C₄	—	2	1	no	—
173	C₁₃×C₂²⋊C₄	—	2	1	no	—
174	C₄²×C₁₃	—	2	4	no	—
175	C₄²×C₁₃	—	2	1	no	—
176	C₄²×C₁₃	—	2	1	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	—	2	2	no	—
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
183	#3503	C₂×C₁₃	1	1	yes	characteristic
184	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#3079	C₂×C₁₃	1	1	yes	characteristic
187	#1649	C₂×C₁₃	1	4	yes	complemented
188	#1648	C₂×C₁₃	1	4	yes	complemented
189	#1549	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#1476	C₂×C₁₃	1	1	yes	characteristic
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	#120	1	1	yes	characteristic
194	Q₈×C₁₃	—	2	1	no	—
195	Q₈×C₁₃	—	2	4	no	—
196	Q₈×C₁₃	—	4	4	no	—
197	Q₈×C₁₃	—	4	2	no	—
198	Q₈×C₁₃	—	4	4	no	—
199	Q₈×C₁₃	—	8	2	no	—
200	Q₈×C₁₃	—	8	2	no	—
201	Q₈×C₁₃	—	8	4	no	—
202	Q₈×C₁₃	C₂×Q₁₆	1	2	yes	—
203	D₄×C₁₃	—	2	4	no	—
204	D₄×C₁₃	—	2	1	no	—
205	D₄×C₁₃	C₂×Q₁₆	1	2	yes	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	8	2	no	—
219	C₂×C₄×C₁₃	—	8	4	no	—
220	C₂×C₄×C₁₃	—	8	2	no	—
221	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
222	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
223	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
225	C₂×C₄×C₁₃	#137	1	2	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₈×C₁₃	—	2	4	no	—
230	C₈×C₁₃	—	4	2	no	—
231	C₈×C₁₃	—	4	2	no	—
232	Q₈²	—	2	1	no	—
233	#557	C₂²×C₁₃	1	2	yes	—
234	#554	—	2	1	no	—
235	#554	—	2	2	no	—
236	D₄×Q₈	—	2	2	no	—
237	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
238	#544	—	2	2	no	—
239	#544	—	2	1	no	—
240	#533	—	2	1	no	—
241	#533	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	—	2	1	no	—
243	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
245	#520	—	2	1	no	—
246	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
247	#500	—	2	2	no	—
248	#500	C₂²×C₁₃	1	4	yes	—
249	#494	—	2	1	no	—
250	#487	—	2	1	no	—
251	#477	—	2	1	no	—
252	#476	—	2	1	no	—
253	#475	C₂²×C₁₃	1	2	yes	—
254	#474	C₂²×C₁₃	1	2	yes	—
255	#462	C₂²×C₁₃	1	4	yes	—
256	#451	—	2	2	no	—
257	#431	C₂²×C₁₃	1	1	yes	characteristic
258	#428	—	2	1	no	—
259	C₂×#107	—	2	2	no	—
260	#423	C₂²×C₁₃	1	1	yes	characteristic
261	#417	—	2	1	no	—
262	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
263	#332	C₂²×C₁₃	1	4	yes	—
264	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
265	Q₈⋊C₈	C₂²×C₁₃	1	4	yes	—
266	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
267	C₂²×C₁₃	—	2	1	no	—
268	C₂²×C₁₃	—	2	1	no	—
269	C₂²×C₁₃	—	2	2	no	—
270	C₂²×C₁₃	—	4	1	no	—
271	C₂²×C₁₃	—	4	1	no	—
272	C₂²×C₁₃	#451	1	2	yes	—
273	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
274	C₄×C₁₃	—	2	2	no	—
275	C₄×C₁₃	—	2	1	no	—
276	C₄×C₁₃	—	2	1	no	—
277	C₄×C₁₃	—	4	1	no	—
278	C₄×C₁₃	—	4	2	no	—
279	C₄×C₁₃	—	4	4	no	—
280	C₄×C₁₃	—	4	1	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	8	2	no	—
283	C₄×C₁₃	#451	1	2	yes	—
284	C₄×C₁₃	#456	1	2	yes	—
285	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
286	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
287	C₄×C₁₃	#576	1	2	yes	—
288	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
289	C₂²×Q₈	—	2	2	no	—
290	C₂²×Q₈	—	2	1	no	—
291	C₂²×Q₈	—	2	1	no	—
292	C₂×Q₁₆	—	2	4	no	—
293	C₂×M₁₆	—	2	1	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	2	4	no	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
306	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
307	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
308	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
309	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
310	#125	—	2	2	no	—
311	#125	—	2	4	no	—
312	#125	—	2	2	no	—
313	#125	—	2	1	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	—	2	4	no	—
316	C₂²⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
326	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
327	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
328	C₄×D₄	—	2	4	no	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	—	2	1	no	—
332	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
333	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
334	#117	—	2	2	no	—
335	#117	—	2	1	no	—
336	#117	—	2	1	no	—
337	#117	D₄×C₁₃	1	1	yes	characteristic
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
346	#107	—	2	8	no	—
347	#107	—	2	2	no	—
348	#106	—	2	2	no	—
349	C₄⋊C₈	—	2	1	no	—
350	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
351	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
352	#103	—	2	2	no	—
353	#103	—	2	4	no	—
354	#102	—	2	2	no	—
355	C₂²⋊C₈	—	2	1	no	—
356	C₄×C₈	—	2	1	no	—
357	C₄×C₈	—	2	1	no	—
358	C₄×C₈	C₂³×C₁₃	1	2	yes	—
359	C₂×C₁₃	—	2	2	no	—
360	C₂×C₁₃	—	4	2	no	—
361	C₂×C₁₃	C₂×#451	1	1	yes	characteristic
362	C₂×C₁₃	#3008	1	1	yes	characteristic
363	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
364	#41	—	2	2	no	—
365	#41	C₁₃×Q₁₆	1	4	yes	complemented
366	C₂×Q₈	—	2	4	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	4	1	no	—
372	C₂×Q₈	—	8	2	no	—
373	C₂×Q₈	—	8	2	no	—
374	C₂×Q₈	—	8	4	no	—
375	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
376	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
388	Q₁₆	—	8	4	no	—
389	M₁₆	—	4	2	no	—
390	C₂×C₈	—	2	4	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₄⋊C₄	—	4	1	no	—
412	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
413	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
414	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
415	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₄²	—	2	4	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	2	no	—
426	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
428	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
430	C₁₃	#18653	1	1	yes	characteristic, direct product factor, Sylow
431	C₂³	—	2	1	no	—
432	C₂³	C₁₃×#120	1	1	yes	characteristic
433	Q₈	—	2	1	no	—
434	Q₈	—	2	4	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	4	no	—
437	Q₈	—	4	4	no	—
438	Q₈	—	8	2	no	—
439	Q₈	—	8	2	no	—
440	Q₈	—	8	4	no	—
441	Q₈	C₂×C₁₃×Q₁₆	1	2	yes	—
442	D₄	—	2	4	no	—
443	D₄	—	2	1	no	—
444	D₄	C₂×C₁₃×Q₁₆	1	2	yes	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	8	2	no	—
458	C₂×C₄	—	8	4	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
461	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
462	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
463	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
464	C₂×C₄	C₁₃×#137	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
468	C₈	—	2	4	no	—
469	C₈	—	4	2	no	—
470	C₈	—	4	2	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	C₁₃×#451	1	2	yes	—
477	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	2	no	—
481	C₄	—	4	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	2	no	—
486	C₄	—	8	2	no	—
487	C₄	C₁₃×#451	1	2	yes	—
488	C₄	C₁₃×#456	1	2	yes	—
489	C₄	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
490	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
491	C₄	C₁₃×#576	1	2	yes	—
492	C₂	—	2	2	no	—
493	C₂	—	4	2	no	—
494	C₂	C₂×C₁₃×#451	1	1	yes	characteristic
495	C₂	C₁₃×#3008	1	1	yes	characteristic
496	C₂	C₂×C₁₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃×#3209	C₂	semidirect
3. C₂×C₁₃×#500	C₂	semidirect
5. C₁₃×#1649	C₂	semidirect
6. C₁₃×#1648	C₂	semidirect
7. C₁₃×#1549	C₂	semidirect
8. C₁₃×#1493	C₂	semidirect
116. #18653	C₁₃	direct (N × H)
118. C₁₃×#41	Q₁₆	semidirect
184. #3209	C₂×C₁₃	semidirect
185. C₂×#500	C₂×C₁₃	semidirect
187. #1649	C₂×C₁₃	semidirect
188. #1648	C₂×C₁₃	semidirect
189. #1549	C₂×C₁₃	semidirect
190. #1493	C₂×C₁₃	semidirect
365. #41	C₁₃×Q₁₆	semidirect
430. C₁₃	#18653	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3503	2
C₁₃×#3209	2
C₂×C₁₃×#500	2
C₁₃×#3079	2
C₁₃×#1649	2
C₁₃×#1648	2
C₁₃×#1549	2
C₁₃×#1493	2
C₁₃×#1476	2
#18653	13

Subgroups — C13×#18653 #15704992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18653 #15704992